`{:("Column A"," ","Column B"),((6^4)/(3^2),,2^4 cdot 3^2):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to evaluate the expressions in Column A and Column B separately and then compare their values.

### Step 1: Evaluate Column A
Column A is given as:
\[ \frac{6^4}{3^2} \]

First, we can calculate \(6^4\) and \(3^2\):
\[ 6^4 = 6 \times 6 \times 6 \times 6 = 1296 \]
\[ 3^2 = 3 \times 3 = 9 \]

Now, substitute these values back into the expression:
\[ \frac{6^4}{3^2} = \frac{1296}{9} \]

Now, perform the division:
\[ \frac{1296}{9} = 144 \]

So, Column A evaluates to:
\[ \text{Column A} = 144 \]

### Step 2: Evaluate Column B
Column B is given as:
\[ 2^4 \cdot 3^2 \]

First, we can calculate \(2^4\) and \(3^2\):
\[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \]
\[ 3^2 = 3 \times 3 = 9 \]

Now, substitute these values back into the expression:
\[ 2^4 \cdot 3^2 = 16 \cdot 9 \]

Now, perform the multiplication:
\[ 16 \cdot 9 = 144 \]

So, Column B evaluates to:
\[ \text{Column B} = 144 \]

### Step 3: Compare Column A and Column B
Now we compare the results from Column A and Column B:
\[ \text{Column A} = 144 \quad \text{and} \quad \text{Column B} = 144 \]

Since both columns are equal, we conclude:
\[ \text{Column A} = \text{Column B} \]

### Final Answer
Both columns are equal.